Development of the ElarmS methodology for earthquake early warning: Realtime application in California and offline testing in Japan. Holly M. Brown n, Richard ...... means that ElarmS underestimates the magnitude of the largest. Alum Rock.

such as the San Francisco Bay Area (SFBA) or the Los Angeles Metro- .... Both ml and mh are used by ElarmS to produce the best estimate of mag- nitude. Initially ..... addition, schools receive the warnings allowing children to take cover be-.

Dec 19, 2018 - products can be built to meet those needs, with the ultimate goal of creating value ... free surface sites. With careful ... NETWORK. As of July 2018, MyShake has been downloaded to more than ...... Hooked: How to Build Habit-Forming P

Seismological images of the Earth's mantle reveal three distinct changes in velocity structure, at depths of 410, 660 and 2,700 km. The ®rst two are best explained by mineral phase transformations, whereas the thirdÐthe D0 layerÐprobably re¯ects a change in chemical composition and thermal structure. Tomographic images of cold slabs in the lower mantle, the displacements of the 410-km and 660-km discontinuities around subduction zones, and the occurrence of small-scale heterogeneities in the lower mantle all indicate that subducted material penetrates the deep mantle, implying whole-mantle convection. In contrast, geochemical analyses of the basaltic products of mantle melting are frequently used to infer that mantle convection is layered, with the deeper mantle largely isolated from the upper mantle. We show that geochemical, seismological and heat-¯ow data are all consistent with whole-mantle convection provided that the observed heterogeneities are remnants of recycled oceanic and continental crust that make up about 16 and 0.3 per cent, respectively, of mantle volume.

T

he Earth's mantle comprises 82% of its volume and 65% of its mass. It constitutes virtually all of the silicate part of the Earth, extending from the base of the crust (0.6% of Earth's silicate mass) to the top of the metallic core (Fig. 1). When the core segregated from the silicate and gas of the proto-Earth, it incorporated high concentrations of the siderophile elements, leaving lithophile elements in the silicate mantle. (Words in bold are explained in the glossary; see Box 1.) Thus, the current composition of the mantle has core formation imprinted on itÐas pronounced depletions in, for example, Fe, Ni, S, W, Pt, Au and Pb relative to the chondritic meteorites1,2, which are used to constrain the composition of the whole Earth. Owing to the fractionation of lithophile radioactive parent isotopes such as 238 U and 182Hf from their siderophile daughters 206Pb and 182W, core formation can be dated as the time at which the evolution of the isotopic compositions of Pb and W diverged from the meteorite trend. The result (about 4.5 Gyr ago) corresponds to 50±100 Myr

after the formation of the oldest meteorite bodies in the Solar System3,4. Mantle rocks that occur occasionally at the surface, either as tectonic fragments (kilometre scale) or as inclusions in explosive eruptives (centimetre scale) are predominantly peridotites. One of the main questions facing the Earth sciences is whether a peridotite composition, representative of the upper 150 km of the mantle, can also be assumed to represent the remainder of the mantle down to 2,900 km depth. Many geochemical data suggest not. For example, the current heat ¯ux at the Earth's surface is about 44 TW (44 ´ 1012 W), most of which can be reasonably attributed to radioactive decay of K, U and Th in the mantle5. The upper-mantle source region of mid-ocean ridge basalt (MORB) is depleted in these elements, however, and only produces 2±6 TW. The simplest explanation of the shortfall is that there is a lower layer enriched in the heat-producing elements that is only sporadically involved in the production of surface rocks6±8. Similarly, the ¯ux of the

AK135

0

410 660

Co

Mantle

cru

D"

st

Depth (km)

nt.

2,000

b

Sla

er ow

Core

“L

4,000

’ er’

lay

6,000

vs 0

2

4

vP 6

8

10

12

ρ 14

Velocity, v (km s–1) Density, ρ (g cm –3 ) Figure 1 Speeds of seismic waves in the Earth, showing the major discontinuities at 410 and 660 km depth, and the D0 layer at the base of the mantle. Also shown (right) is a cutaway view of the Earth, showing a region of continental crust and a subducted lithospheric slab extending into the lower mantle. The D0 layer is irregular in thickness. A hypothetical ``lower layer''5 is shown with a dashed line. NATURE | VOL 412 | 2 AUGUST 2001 | www.nature.com

The principal data relating to the deep interior are those of seismology. Global one-dimensional seismic models11 (Fig. 1) clearly show the main features that constrain the mineralogical and chemical constitution of the deep interior. More detailed regional studies provide important additional information. Figure 1 shows that there are two main seismic discontinuities in the mantle, at 410 and 660 km depth. In the lower mantle, below 660 km, seismic velocities increase monotonically with depth until the D0 region is reached at about 200 km above the core±mantle boundary. The latter is a region of low gradient in seismic wave speeds, and contains large-scale low-velocity structures and regional discontinuities12. Although the mantle discontinuities (410, 660 and D0) are all, potentially, due to chemical layering of the mantle, pressure-induced phase transformations in peridotite are more plausible explanations for the two shallower discontinuities. Phase transformations. Bernal13 was the ®rst to propose that rapid increases in seismic velocity in the mantle might be due to phase transformations rather than a change in composition. Experiments in the mid-1960s14 showed that the olivine component of peridotite undergoes successive pressure-dependent transformations to the Box 1 Glossary Basalt A rock made by 5±20% melting of peridotite. It is produced under mid- ocean ridges (mid-ocean ridge basalt, MORB) by upwelling of hot mantle. Ocean island basalts (OIBs) are products of similar processes under ocean islands. Chondritic meteorites A class of meteorites that record the early history of the Solar System. They are thought to represent primitive planetary materials. EM-1, EM-2 basalts OIBs having isotopic similarities to recycled continental materials. HIMU basalts OIBs having isotopic similarities to recycled oceanic crust. Incompatible/compatible When rock starts to melt, some elements (incompatible) are concentrated in the liquid silicate while others (compatible) remain in the solid minerals. Lithophile/siderophile Elements that dissolve readily in metallic iron under moderately reducing conditions are siderophile, and are concentrated in the core. Those that more readily bond with oxygen are lithophile, and are concentrated in the silicate Earth. Peridotites Rocks made up predominantly of olivine (Mg,Fe)2SiO4, with lesser amounts of orthopyroxene (Mg,Fe)SiO3 and clinopyroxene Ca(Mg,Fe)Si2O6. Although rarely found at the surface, they appear to be the dominant rock type of the mantle. Refractory Refractory elements condense from gas to solid at high temperatures.

The transformations of olivine to wadsleyite, and ringwoodite to perovskite (+ oxide), clearly correlate with the two major global seismic discontinuities, and must generate at least some part of the seismic `signal'. But do phase transformations at constant peridotite bulk composition completely explain the seismic phenomena, or are chemical discontinuities also required? Consider the responses of the three transformations to changes in temperature. Figure 2 (ref. 17) shows a pressure±temperature (P±T) diagram for pure Mg2SiO4 that illustrates the main points. The transformation of olivine to wadsleyite has a positive slope, with dP/dT of approximately +3 MPa K-1. In contrast, the breakdown of ringwoodite to perovskite plus magnesiowuÈstite has a negative slope of -2 MPa K-1. Thus, if the 410- and 660-km discontinuities are entirely due to these phase transformations, regions of abnormally low temperature such as subduction zones should correspond to elevation of the `410' to lower depths and depression of the `660' to greater depths. We address the testing of this prediction in the next section. A more direct approach to correlating mineralogy and seismic properties is through the elastic properties of the whole mineral assemblage. This requires consideration of transformations in the non-olivine component (30%) through the transition zone (410± 660 km) and into the lower mantle. Phase changes in the pyroxene and garnet components of mantle peridotite are gradual, and lead to changes in slope of the curves of seismic velocity versus depth rather than to discrete discontinuities. The principal transformations involve, ®rst, dissolution of pyroxene into the garnet structure at pressures corresponding to 350±500 km depth18,19. Then, at about 580 km depth, a few per cent of CaSiO3 perovskite begins to exsolve from the garnet, which at that point constitutes about 30% of a bimineralic (garnet + ringwoodite) mantle:

26 Perovskite + oxide 24 22 Pressure (GPa)

radioactive products 40Ar (from K) and 4He (from U, Th) into the atmosphere should be predictable from the surface heat-¯ow and the approximate abundances of K, U and Th in the bulk Earth. In fact, about 50% of the 40Ar produced over the age of the Earth is missing from the atmosphere9, while the ¯ux of 4He from the oceans is only 5% of that predicted from oceanic heat ¯ow10. These observations again lead naturally to the concept of a region in the deep Earth, rich in the products of radioactive decay, which exchanges heat but little mass with the convecting upper mantle (Fig. 1). The object of this Review is initially to summarize the data relating to the structure and composition of the mantle with an emphasis on those observations in favour of, or against, chemical layering. We will then present some possible ways in which con¯icting evidence might be reconciled, and suggest some future directions that will help resolve the remaining questions.

penetration of slabs into the lower mantle and with deep recycling of former lithospheric material. Global seismic tomographic images, based on both short- and long-period data, also strongly suggest slab penetration into the lower mantle. A variety of modern studies show narrow features of high seismic velocity extending from sites of present-day subduction deep into the lower mantle29,30,42. The implication of these seismological observations, in combination with dynamical modelling of mantle mixing43,44, is that there is no major change of chemical composition between the upper and lower mantles. But in contrast to the well-resolved high-velocity structures extending into the lower mantle, the diffuse form of warm low-velocity structures in tomographic images do not as yet convincingly delineate return ¯ow from the lower to the upper mantle. An important feature of the lower mantle that long-period tomographic studies do not resolve is small-scale elastic heterogeneity, which has been discovered using scattered waves45±48. These studies observed bodies distributed throughout the lower mantle that were smaller than 10 km in size, and whose wave speeds varied by 1% or more from that of the ambient mantle. In the few cases where individual scatterers were identi®able, they had seismic velocities at least 4% slower than their surroundings48 and arrayed themselves in linear structures resembling heterogeneities stretched by convective stirring in the mantle49±51. These `scatterers' must be chemical rather than thermal heterogeneities because they are too small (assuming thermal diffusivity of 1 ´ 10-6 m2 s-1; ref. 52) to maintain a temperature difference from the mantle for longer than about 200,000 years. Given the tomographic evidence for deep subduction, the most likely explanation is that they are remnants of lithospheric slabs. Substantial changes in seismic wave speeds occur locally in the lowermost part of the mantle, D0. This approximately 200-km-thick region varies in thickness, and contains discrete discontinuities53, scattering features46,54±56, and possibly, thin low-velocity layers against the core±mantle boundary57,58. D0 is also anisotropic, and the variations in P-wave and S-wave speeds are uncorrelated59,60. In combination, these features suggest that D0 is a region with pronounced lateral chemical heterogeneity that differs chemically from the overlying mantle. These seismological properties of mantle structure may be summarized in a map (Fig. 3) of the angular correlation function of seismic heterogeneity provided by analysing recent mantle tomographic studies61. The angular correlation function reveals the lateral extent of correlated variations in wave speed at a given depth in the mantle. Lateral heterogeneity in the upper mantle is signi®cant, and is organized into broad regions (continents and oceans)60, shown by the wide correlation lengths. In the lower mantle, the correlation length diminishes to an approximately constant level until the base of the mantle is approached, when it increases again owing to the structure of D0. There are no changes in correlation length in the lower mantle attributable to boundaries between elastically different material. Thus, whatever heterogeneity is present in the lower mantle, the observational seismic data only require it to be homogeneously distributed, without undergoing any signi®cant scale reorganization with depth. In summary, modern seismological studies show that the mantle is chemically heterogeneous at the 10-km length scale, but give no clear evidence of radial strati®cation other than at the boundary with the D0 region. Both tomographic and seismic array studies are consistent with deep subduction and hence with whole-mantle convection.

Heat ¯ow and geochemistry

Current global heat loss is 44.2 ´ 1012 W (44.2 TW)62. This is made up of contributions from radioactive decay of K, U and Th and from secular cooling of the Earth. Measurements of the compositions of the most primitive, unfractionated, mantle peridotites indicate that

review article refractory lithophile elements such as Ca, Sc, Ti, the rare-earth elements (REE), U and Th are in chondritic ratio one to another in the silicate part of the Earth1,63. This leads to concentrations of about 20 p.p.b. (parts per billion) U and 80 p.p.b. Th in bulk silicate Earth (that is, mantle + crust). Chemical analysis of igneous rocks indicates that their K/U ratios are generally about 12,500, irrespective of rock type or tectonic settting64. This implies a K content of bulk silicate Earth of about 12,500 times the U content, or 250 p.p.m. This inventory of radioactive elements is at present producing 20 TW, or about 45% of the total heat ¯ow65. But the mantle has a long thermal time constant, and advective removal of heat is linked to the vigour of plate-tectonic motions that vary over time, so that the heat loss measured now was generated by decay in the distant past. Although the age of the current heat-loss is, of course, modeldependent, we can make defensible estimates based on the apparent ages of isotopic heterogeneities in the mantle, such as those of modern HIMU basalts8. These are being generated now from melting of oceanic crust that was recycled from the surface into the deep interior 1±2 Gyr ago. Using the latter ®gures as a measure of the age of the heat reaching the surface yields a radioactive heat contribution of 24.9±32.9 TW (ref. 65). Parametrized convection models of the cooling of the Earth's interior yield secular cooling rates of 30±100 K Gyr-1 (refs 66, 67). This loss of the Earth's heat energy produces heat ¯uxes between 5.9 and 20 TW, which are capable of making up the balance from the geochemically inferred radioactive heat production. By mass-balancing the different parts of the silicate Earth to the overall bulk silicate composition1, we can determine how much `hidden' layering is necessary to make the whole. We will concentrate on the heat-producing elements, and begin by considering two major reservoirs whose concentrations of K, U and Th are reasonably well-knownÐthe continental crust68 and the mantle source of MORB69. From the major-element compositions of MORB, it appears that these voluminous volcanic rocks are produced by about 10% melting of peridotite mantle70,71. Assuming that K, U and Th act as incompatible elements, this means that the mantle

40°

30°

50°

60°

20°

70°

° 10

0°

40° 50° 60°

70°

–1.0 –0.5 0.0 0.5 1.0

(k m )

30°

80 °

h

20°

De pt

0 0 2,

5 C 00 M B

1, 50

2, 00

° 10

0 41 60 0 6 0 0 1, 0 50 1, 0 00 2, 0 50 2, B M C ° 90

41 1, 660 0 00 0

° 90

0°

80 °

th

m )

(k

De p

Correlation coefficient

Figure 3 Angular correlation function of a shear-wave tomographic model30 as a function of depth. This characterizes the similarity of wave speed of two points at the same depth in the mantle separated by some angular distance. Every point in the mantle is perfectly correlated with itself, resulting in the maximum correlation for points separated by zero distance (left side of ®gure). A drop of e-1, or about 0.4, indicates a signi®cant correlation decrease (the yellow band). Blue colours representing zero or negative correlations arise at large separations, and a degreetwo pattern at the mantle's base is made evident by the maximum negative correlation at ,908. The correlation length is greatest in the upper mantle and in D0. In the upper mantle, this probably corresponds to continent/ocean differences60, while the structure in D0 possibly re¯ects the pattern of heat ¯ow out of the core into the mantle. In the lower mantle above D0 the correlation length is approximately constant, indicating no reorganization of heterogeneity scale length in the mid±lower mantle. CMB, core±mantle boundary. 504

contains about 0.1 times the concentrations found in MORB. In that case the mantle source can only have about one-third the concentrations of K, U and Th (and other incompatible elements) postulated for the bulk silicate Earth1. It is therefore `depleted' mantle. As the continental crust is highly enriched in these incompatible elements, the simplest assumption is that enriched crust and depleted mantle are complementary, and formed by differentiation of bulk silicate Earth69. The result (Table 1) indicates that there is insuf®cient enriched crust for the depleted peridotite mantle to comprise the whole mantleÐit turns out to constitute only 50% of the whole mantle. The calculation can be repeated with isotope systems such as Sm±Nd with very similar results72. Mantle layering (Fig. 1) is the logical conclusion. The simple layered model is, however, compromised by seismological evidence in favour of whole-mantle convection, or at least of deep subduction of slabs into the lower mantle and of heterogeneities introduced by subduction. That these heterogeneities are real and long-lasting is attested to by seismological evidence of lowermantle `scatterers', and by enriched ocean island basalts (OIBs) that contain isotopic evidence of contributions from old subducted oceanic crust (HIMU) and from continental crust and lithosphere (EM-1, EM-2)8. The current rate of subduction73 of 3 km2 per year means that approximately 18 km3 of oceanic crustÐand, assuming 10% melting by mass, 140 km3 of highly depleted, `sterile' peridotiteÐis being returned to the mantle each year. Rather more dif®cult to estimate is the amount of continental sediment that is returned to the mantle with the subducted oceanic plates. Recent estimates vary between 0.7 and 1.5 km3 per year74. Therefore, assuming a constant rate of subduction for 4 Gyr, we ®nd that the mantle contains 5% recycled oceanic crust, 45% recycled `sterile' mantle and about 0.3% recycled continental material. If the higher rate of heat production in the past (3.6 times current values at 4 Gyr ago) was compensated by higher heat loss through formation of oceanic lithosphere, then it seems likely that almost the entire mantle has been through the cycle of partial melting, oceanic crust formation and sediment recycling. In that case a better view of the mantle today would be as a heterogeneous mixture of `sterile' highly depleted mantle containing `blobs' of oceanic and continental crust of different ages and sizes. Such `blobs' are real, and recorded as chemical heterogeneities in studies of scattered seismic waves. In Fig. 4 we show how a heterogeneous model of the mantle would ®t with the chemical composition of the silicate Earth. Assuming that there is no primitive undepleted mantle, the silicate Earth consists of continental crust (0.6% by mass), `sterile' mantle (. 45%), and recycled continental and oceanic material. As the depleted mantle produces basalt by about 10% partial melting70,71, we can consider it a mixture of 10% recycled oceanic crust and 90% `sterile' peridotite. There are two end-member approaches for massbalancing K, U and Th in the silicate Earth that differ in their complexity. Either yields agreement with K, U and Th abundances, so we consider the differences they predict in other trace-element abundances to discriminate between them. One end-member assumes that average rates of oceanic crust production over the past 4 Gyr were twice the present rate, processing the whole mantle through the MORB production process, with 0.4% recycled continental crust material. The other end-member assumes a lower rate

review article of oceanic crust production, no recycled continental crust, and that the 16% remaining, yet-to-be-processed mantle mass fraction is excessÐor `old'Ðmaterial left over from an episode of early differentiation and oceanic crust extraction, as Hf isotope evidence suggests75. In either case, modern MORB comes from a `marblecake'50 mixture of `sterile' mantle and recycled oceanic crust. OIB has a similar origin, but the melting process must involve more of the recycled oceanic and continental crust in order to generate its higher incompatible trace-element content8,50. We can test the two end-members by mass-balancing the bulk silicate Earth contents of elements such as Ti, Zr and La, which are geochemically similar to K, U and Th. The end-member with no `old' recycled oceanic crust requires about 1% additional oceanic crust to mass-balance (Fig. 4). The end-member with `old' excess crust overestimates the trace element abundances by an amount equivalent to 10% additional oceanic crust. Best overall agreement is achieved with a 75%/25% mixture of the end-member models (0.3% recycled continental material and 5% `excess' recycled oceanic crust). In either, the recycled material in depleted mantle (.90% of the mantle) is

Figure 4 Approximate mass balance for a bulk silicate Earth made up of continental crust, `sterile' mantle, recycled oceanic crust, old recycled oceanic crust, and recycled continental material. The proportions satisfy seismological, heat-¯ow and most traceelement geochemical constraints. Diagrams at bottom show mis®t to trace-element abundances if the total amount of recycled oceanic crust is varied. The large Nb value is symptomatic of the ``missing niobium problem''8,87. Ba and Rb values are very sensitive to the amount of recycled continental crust and to unknown effects of subduction zone ¯uids. NATURE | VOL 412 | 2 AUGUST 2001 | www.nature.com

Figure 5 Visibility of mantle heterogeneity by seismic scattering. The abundance of mantle heterogeneities decreases with size exponentially (left axis), while the scattering power increases with the cube of the scatterer size (right axis). Scatterers smaller than ,4 km are not likely to be visible on account of the attenuation of highfrequency body waves in the upper mantle (wavenumber k ~ frequency) that would be sensitive to them. Consequently, only the largest mantle heterogeneities yield observable scattering. With values of k = 2.25 ´ 10-3 km-1 and f0 = 2.04 ´ 10-3 that satisfy the observational scattering constraints and the abundance of non-`sterile' mantle components, 93 vol.% of heterogeneity should be , 4 km in size, and hence invisible to seismic scattering.

Models of the convective stretching and dispersal of heterogeneities indicate that average size becomes smaller with time, with an exponential dependence of fractional volume f on size a (ref. 49): f(a) = f0 exp(-ka). The unknowns f0 and k can be constrained because the integral of f over heterogeneity sizes 0±8 km must yield the volume fraction of the mantle occupied by heterogeneities (around 11±16% from geochemical arguments). Also, the fraction at a = 8 km must agree with the number of seismically observed heterogeneities of that size. The latter is unknown, because much of the mantle has yet to be systematically explored for scatterers, but it should be of the order of the volume of subducted oceanic crust currently en route to the base of the mantle. This volume is about 0.2% of the mantle, assuming the present global rate of mass transfer into subduction zones and a vertical descent rate in the mantle of 30 mm yr-1 (refs 30, 48). Both constraints are satis®ed by k = 2.25 ´ 10-3 km-1 and f0 = 2.04 ´ 10-3, leading to the prediction that 93% (by volume) of the heterogeneity is smaller than 4 km, which would be invisible to short-period wave scattering (Fig. 5). From a seismological viewpoint, the mantle therefore appears to exhibit an overlapping collection of vertically homogeneous regions that coexist with heterogeneity on a range of length scales (Fig. 6). However, most of the heterogeneity volume is represented by very small bodies (, 4 km). This homogeneous distribution of heterogeneity extends from the base of the mantle into the MORB melting region, 40±80 km below the surface, where it is destroyed by melting and melt extraction. The latter melting region acts as a near-surface `heterogeneity sink'Ðthe larger heterogeneities can only be inferred from their chemical signatures. Despite having to traverse the region of homogenization, however, large peridotite bodies tectonically emplaced in the continental crust still exhibit a wide range of metreand centimetre-scale heterogeneities82,83.

Perspective and outstanding problems

Early interpretations of the seismic structure of the Earth, incorporating what was known about the compositions of meteorites, suggested a gradual change from silicate to iron-rich compositions with depth. This view was abandoned in favour of a layered mantle, once the nature of the core±mantle boundary was recognized, and ®nite strain theories became available to model changes in material elasticity with depth. The seismic discontinuities at 410 and 660 km 506

Figure 6 Sketch of proposed model of a chemically unstrati®ed mantle. Subduction of oceanic lithosphere introduces heterogeneity into the mantle. Mixing by convective stirring of the mantle disaggregates the subducted lithosphere and minor continental material, producing isolated heterogeneities that scatter seismic energy but are too small to be observed tomographically. Melting at mid-ocean ridges and at ocean islands produces basalts and homogenizes the two types of mantle material, one enriched in incompatible elements and the other `sterile'.

depth initially appeared to be likely boundaries for the compositional layering. Recent studies of discontinuity topography and tomographic images of slab penetration into the lower mantle have, however, forced revision of this view. The latter results are most consistent with the discontinuities corresponding to phase transformations under isochemical conditions in a peridotite mantle. Strati®cation seems, therefore, to be an increasingly dif®cult position to defend. Lateral heterogeneity is, however, well established in the upper mantle, and has recently been shown to be present in the lower mantle. The principal issue is becoming how to interpret the heterogeneity seen at all depths in the mantle and to integrate it with the Earth's chemical composition. We have presented here a simple geochemical model based on four componentsÐ`sterile' peridotite, recycled oceanic crust, and continental crust part of which is recycledÐthat is one way to explain most of the geophysical and geochemical observations. With present techniques, seismic tomography, which averages over large volumes in the lower mantle, cannot resolve heterogeneities smaller than 400 km in size. Scattering, however, probes subwavelength scales in the mantle (,10 km), and the challenge will be to integrate this into whole-Earth studies. The aim now, guided by convective mixing models, will be to decipher the style and rate of mantle mixing, placing constraints on the residence times of the chemical components of the mantle in their respective reservoirs. The challenge to experimental and isotope geochemists is clearly to understand better the sources and sinks of rare gases in the Earth, and the mechanisms by which they are extracted from the mantle M and deposited in the atmosphere. 1. McDonough, W. F & Sun, S.-S. The composition of the Earth. Chem. Geol. 120, 223±253 (1995). 2. Newsom, H. E. in Global Earth Physics: Handbook of Physical Constants Vol. 1 (ed. Ahrens, T. J.) 159±189 (Reference Shelf Series, American Geophysical Union, Washington DC, 1995). 3. AlleÁgre, C. J., ManheÁs, G. & Gopel, C. The age of the Earth. Geochim. Cosmochim. Acta 59, 1445±1456 (1995). 4. Halliday, A., RehkaÈmper, M., Lee, D.-C. & Yi, W. Early evolution of the Earth and Moon: New constraints from Hf-W isotope geochemistry. Earth Planet. Sci. Lett. 142, 75±89 (1996). 5. Kellogg, L. H., Hager, B. H. & van der Hilst, R. D. Compositional strati®cation in the deep mantle. Science 283, 1881±1884 (1999). 6. Schilling, J.-G. Iceland mantle plume: geochemical evidence along Reykjanes Ridge. Nature 242, 565± 571 (1973). 7. AlleÁgre, C. J., Staudacher, T. & Sarda, P. Rare-gas systematicsÐformation of the atmosphere, evolution and structure of the Earth's mantle. Earth Planet. Sci. Lett. 81, 127±150 (1987). 8. Hofmann, A. W. Mantle geochemistry: the message from oceanic volcanism. Nature 385, 219±229 (1997). 9. AlleÁgre, C. J., Hofmann, A. W. & O'Nions, R. K. The argon constraints on mantle structure. Geophys. Res. Lett. 23, 3555±3557 (1996). 10. O'Nions, R. K. & Oxburgh, R. Heat and helium in the Earth. Nature 306, 429±431 (1983).